Calibrating Rothermel’s fuel models by genetic algorithms

Abstract

A new method to customize Fire Behaviour Fuel Models was developed by linking Genetic Algorithms (GA) to the Rothermel’s equation implemented in the Rothermel package for R. GA randomly generates solutions of fuel model parameters to form an initial population. Each solution is validated against observations of fire rate of spread (ROS) via a goodness-of-fit metric (i.e., RMSE). The population is then selected for its best members, crossed over, and mutated within a range of fuel model parameters space, until fitness is maximized. We tested the performance of GA-optimization against custom fuel models calibrated in two previous studies in grass and shrub fuels. GA was constrained using fuel parameters ranges reported in the selected studies, and was fit against the published ROS measurements. We compared goodness-of-fit (RMSE; R2adj) of fuel models calibrated by GA against that of the original studies. GA improved the fit of Rothermel’s model for both studies: RMSE decreased from 5.5 to 4.6 m/min and from 6.9 to 5.4 m/min, respectively for grass and shrub fuel models. R2-adj increased from 0.83 to 0.84, and from 0.73 to 0.83, respectively. We then ran GA-optimization to calibrate a Calluna heaths fuel model against ROS and environmental data measured under experimental conditions. We obtained ranges of fuel model parameters (fuel load; fuel structure) by a field survey in both experimental plots and other Calluna sites of North-West Italy. Ranges of fuel flammability parameters were derived from the literature. We divided fire experiments into a calibration and a validation dataset (20 ROS each) and ran GA-optimization on the calibration dataset to customize the Calluna fuel model. We predicted ROS in the validation dataset by running the Rothermel modelon each of the following fuel models: i) GA-optimized fuel model; ii) the Standard Fuel Model which minimized RMSE against observations; iii) custom fuel models for Calluna heaths, parameterized using modal values from the overall fuel inventory, or inventoried at each experimental plot. Predictions of the Rothermel model reformulation implemented in FCCS, using as input modal values at the vegetation complex or at plot scale, were also evaluated. ROS predictions obtained by GA-optimized fuel model against the calibration dataset had a RMSE of 1.66 m/min and R2-adj of 0.96. When tested against the validation dataset, GA-optimized fuel model produced the lowest prediction error of all the alternative fuel models (RMSE = 1.74 m/min R2-adj = 0.90). FCCS predictions produced RMSE= 3.76 and 2.24 m/min, respectively using modal values from the fuel complex or at the plot scale, and R2-adj= 0.86 in both cases. GA-optimization provided an objective and accurate calibration of custom fuel models. It can be implemented in several fire prediction systems based on the Rothermel model, including the Rothermel package for R. Increasing the range of fuel model parameters beyond the measured values (e.g., +25%, +50%) can further improve GA model performance. However, this raises the question on how far apart from the field truth a fire behaviour fuel model should be stylized.